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The magnitude, or size, of a vector a\underline{i}+b\underline{j} in 2 dimensions is found by the formula: \sqrt{(a^2+b^2)}
The magnitude, or size, of a vector a\underline{i}+b\underline{j}+c\underline{k} in 3 dimensions is found by the formula: \sqrt{(a^2+b^2+c^2)}
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Summary/Background

The formula for the magnitude of a vector is basically Pythagoras' theorem extended to 3 dimensions.

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Glossary

magnitude

A measure of the size of a mathematical object

union

The union of two sets A and B is the set containing all the elements of A and B.

vector

A mathematical object with magnitude and direction.

Full Glossary List

This question appears in the following syllabi:

SyllabusModuleSectionTopic
AQA A-Level (UK - Pre-2017)C4VectorsVector algebra
AQA A2 Maths 2017MechanicsKinematics3D Vectors
AQA AS Maths 2017MechanicsVectorsVector Basics
AQA AS/A2 Maths 2017MechanicsVectorsVector Basics
CBSE XII (India)Vectors and 3-D GeometryVectorsTypes, equal, unit, parallel, collinear
CCEA A-Level (NI)C4VectorsVector algebra
CIE A-Level (UK)P1VectorsVector algebra
J VectorsJ3 Basic Operations and DiagramsVector Algebra
Edexcel A-Level (UK - Pre-2017)C4VectorsVector algebra
Edexcel A2 Maths 2017Pure MathsVectors3D Vectors
Edexcel AS Maths 2017Pure MathsVectorsVector Basics
Edexcel AS/A2 Maths 2017Pure MathsVectorsVector Basics
I.B. Higher Level4VectorsVector algebra
I.B. Standard Level4VectorsVector algebra
Methods (UK)M4VectorsVector algebra
OCR A-Level (UK - Pre-2017)C4VectorsVector algebra
OCR A2 Maths 2017Pure MathsVectors3D Vectors
OCR AS Maths 2017Pure MathsVectorsVector Basics
OCR MEI A2 Maths 2017Pure MathsVectors3D Vectors
OCR MEI AS Maths 2017Pure MathsVectorsVector Basics
OCR-MEI A-Level (UK - Pre-2017)C4VectorsVector algebra
Pre-Calculus (US)E1VectorsVector algebra
Pre-U A-Level (UK)6VectorsVector algebra
Scottish (Highers + Advanced)HM3VectorsVector algebra
Scottish HighersM3VectorsVector algebra
Universal (all site questions)VVectorsVector algebra
WJEC A-Level (Wales)C4VectorsVector algebra